Perturbações unitárias multiplicativas - Díaz, Pablo (Universidade Federal de São Carlos, 2023)
For the self-adjoint operator H, the perturbation H+A, with A also a self-adjoint operator, there is a long list of results regarding the spectrum of this perturbation. We study the spectrum of a multiplicative perturbation XU (UX) with U and X unitary operators. Specifically, we find similar results for the Howland, Weyl-von Neumann Theorems and the continuous singular spectrum for a perturbation of rank one.
Unitary multiplicative perturbation
Keywords: Operadores auto-adjuntos; Operadores unitários; Perturbações multiplicativas; Decomposição espectral; Teorema de Birman-Krein; Teorema de Weyl-von Neumann; Teorema de Howland; Self-adjoint operators; Unitary operators; Multiplicative perturbations; Spectral decomposition; Birman-Krein Theorem; Weyl-von Neumann Theorem; Howland Theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::FISICA MATEMATICA